Rates
What is the difference between a ratio and a rate?
A rate is a comparison of one quantity of one unit to 1 of another unit.
Which equations represent a proportional relationship? [select all]
A. y=3x
B. y=12x-5
C. y=15/x
D. y=2x+1
E. y=0.2x
A and E
y=2.5x
Solve when x=40
y=100
What are the two qualities a graph needs to have to show that it represents a proportional relationship?
The graph is a straight line.
The graph goes through the origin (0,0).
A recipe calls for 2 and 1/2 cups of sugar to make 2 gallons of sweet tea. How many cups are needed to make 5 gallons of sweet tea?
6 and 1/4 cups are needed to make 5 gallons of sweet tea.
Mr. Hess drives 256 miles in 4 hours. How fast was he driving?
64 miles per hour (mph)
Given the following values for x and y tell if there is a proportional relationship. Also, why or why not?
x: 5, 10, 15, 20
y: 3, 6, 9, 15
No because the last pair of x and y are not proportional to the rest.
y=7x
What is the value of k?
k=7
A graph shows the relationship between the number of cans (x) and the number of tennis balls (y). What does the point (0,0) represent?
The point (0,0) represents 0 cans and 0 tennis balls.
At a clothing store, 4 shirts cost $51.96. How much would 7 shirts cost?
7 shirts will cost $90.93
Laura walks 6 miles in 1.5 hours. Sasha walks 2.5 miles in 1/2 hour. Who walks faster?
Sasha walks faster because she walks 5 miles per hour. Laura walks 4 miles per hour.
The relationship between x and y is proportional. When x=5, y=45. When y=216, what is x?
x=24
k=2/1
or
k=2
Draw a graph of a proportional relationship that passes through the point (3, 4).
Instructor will check
Morgan and Craig painted 432 in2 of a canvas with 1/2 quart of paint. How many in2 can they paint with 3 quarts of paint?
2592 in2 of canvas.
Julissa typed 2 pages of a paper in 9 and 1/3 minutes. What is her typing speed in minutes per page?
4 and 2/3 minutes per page
Tony knows he is 45 meters from school. The map on his phone shows that the school is 3/5 of an inch from his current location. If Tony's house is 2 inches from his current location, how many meters is he from home?
150 meters from home
The point (5,2) is on the graph of a proportional relationship. What is the equation of the line?
y=2.5x
A straight line passes through the point (0,7). Does this graph represent a proportional relationship?
No because it does not go through the origin.
A group of 9 people are going bowling. Strike Zone costs $29.01 for 3 games. Lucky Lanes costs $39 for 4 games. If they bowl 5 games, how much will the group save by going to Strike Zone?
The group saves $3.60.
In a bakery, the ratio f chocolate bars to cupcakes is 7:4. The bakery makes 56 chocolate bars on Tuesday morning.
If they sell half of their chocolate bars and cupcakes, will the ratio change? (y/n)
After the sale of half their inventory, there are ____ chocolate bars and _____ cupcakes.
There are 28 chocolate bars and 16 cupcakes.